An Exact Solution For Modeling Photoacclimation of the Carbon-to-Chlorophyll Ratio in Phytoplankton

A widely-used theory of the photoacclimatory response in phytoplankton has, until now, been solved using a mathematical approximation that puts strong limitations on its applicability in natural conditions. We report an exact, analytic solution for the chlorophyll-to-carbon ratio as a function of the dimensionless irradiance (mixed layer irradiance normalized to the photoadaptation parameter for phytoplankton) that is applicable over the full range of irradiance occurring in natural conditions. Application of the exact solution for remote-sensing of phytoplankton carbon at large scales is illustrated using satellite-derived chlorophyll, surface irradiance data and mean photosynthesis-irradiance parameters for the season assigned to every pixel on the basis of ecological provinces. When the exact solution was compared with the approximate one at the global scale, for a particular month (May 2010), the results differed by at least 15% for about 70% of Northern Hemisphere pixels (analysis was performed during the northern hemisphere Spring bloom period) and by more than 50% for 24% of Northern Hemisphere pixels (approximate solution overestimates the carbon-to-chlorophyll ratio compared with the exact solution). Generally, the divergence between the two solutions increases with increasing available light, raising the question of the appropriate timescale for specifying the forcing irradiance in ecosystem models